A Gambit is any action made to achieve some kind of advantage, usually requiring some degree of risk.
A gambit is a gamble, isn't it? Something harmful/risky to one's agenda which hopefully pays off?
A gambit can be something as simple as the Doctor saying "The doctor should protect so-and-so tonight." to a full-blown WIFOM designed to mislead, incriminate, corroborate, or otherwise change the game; the trick is not getting caught doing it. A high-risk, high-reward move, in other words.
"Well, I was just gambiting, I'm not tracker, I'm a Cop with a guilty result on you. Thanks for claiming the kill, though."
--Textbook Scenario of Kokusho's Gambit